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Using the first-principles exact muffin-tin orbital method in combination with the coherent potential approximation, the crystal structure and site preference, magnetic and elastic properties, and martensitic transformation (MT) are systematically investigated with the three groups of Heusler alloys: (Co[Formula: see text]M[Formula: see text])VGa (M1[Formula: see text]), Co[Formula: see text](V[Formula: see text]M[Formula: see text])Ga (M2[Formula: see text]), and Co[Formula: see text]V(Ga[Formula: see text]M[Formula: see text]) (M3[Formula: see text], M = Ni and Fe, [Formula: see text]). It is shown that instead of the [Formula: see text] and [Formula: see text]A structures, the fcc one is energetically preferred in the cubic M3 x ([Formula: see text]) alloys. In [Formula: see text]-Ni2 x ([Formula: see text]) and fcc-Ni3 x ([Formula: see text]), Ni atoms even prefer the Ga and Co anti-sites, respectively, and the replaced atoms move to the sublattices of the deficient ones. Their total magnetic moment is dominated by the magnetic exchange interactions corresponding to the pairs of two Co atoms on the different sublattices in M = Ni and Fe1 x, Co and Fe in Fe2 x and Fe3 x ([Formula: see text]), and Fe and Fe atoms in Fe3 x ([Formula: see text]) alloys, respectively. These Ni1 x, Ni2 x, and Fe3 x with [Formula: see text] as well as Ni3 x with [Formula: see text] alloys are predicted having the MT behavior and also the better mechanical property relative to Co[Formula: see text]VGa. A lower shear modulus ([Formula: see text]) generally corresponds to a higher MT temperature, and these alloys, which can undergo the MT are further evaluated with [Formula: see text] GPa. Both considerable magnetocaloric and magnetovolume effects can be also expected during the MT of these Fe3 x alloys ([Formula: see text] and 0.6). In the remaining Fe1 x and Fe2 x alloys, the Fe doping disfavors the MT and also improves their brittleness. The structural preference of these cubic alloys and also their stability relative to the tetragonal martensite can be mainly attributed to the number of their minority density of states at the Fermi level: the smaller they are, the more stable their system tends to be.

The alloying and magnetic disordering effects on the site occupation, elastic property, and phase stability of Co2 YGa (Y=Cr, V, and Ni) shape memory alloys are systematically investigated by using the first-principles exact muffin-tin orbitals method. It is shown that with increasing the magnetic disordering degree (y), their tetragonal shear elastic constant C' ((C 11 - C 12)/2) of the L21 phase decreases whereas the elastic anisotropy (A) increases, and upon tetragonal distortions the cubic phase gets more and more unstable. Co2CrGa and Co2VGa alloys with y ≥ 0.2 thus can show the martensitic transformation (MT) from L21 to D022 as well as Co2NiGa. In off-stoichiometric alloys, the site preference is controlled by both the alloying and magnetic effects. At the FM state, the excess Ga atom always tends to take the Y sublattice, whereas the excess Co atom favors the Y site when Y=Cr, and the excess Y atom prefers the Co site when Y=Ni. The Ga-deficient Y=V alloys can occur the MT also at the FM state by means of Co or V doping, and the MT temperature (T M ) should increase with their addition. In the corresponding FM Y=Cr alloys, nevertheless, with Co or Cr substituting for Ga, the reentrant MT (RMT) from D022 to L21 is promoted and then T M for the RMT should decrease. The alloying effect on the MT of these alloys is finally well explained by means of the Jahn-Teller effect at the paramagnetic (PM) state. At the FM state, it may originate from the competition between the austenite and martensite about their strength of the covalent banding between Co and Ga as well as Y and Ga.

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